A power-law exponential model for variograms with quick transition and known range: Construction and application to geostatistical time series

The variogram is an important element in geostatistical studies that has been used as a tool to investigate the variability and continuity of the study phenomenon. The classical Matheron estimator for calculating the experimental variogram is used in this paper. A new variogram model is proposed, the power-law exponential model and a comparative study of three-time series datasets with the characteristic of being periodic is performed: rainfalls, particulate matter PM10, and Ozone series. Three other models were considered for comparison: spherical, exponential, and quadratic-exponential. The numerical fit and analysis are carried out using the least-squares method provided by the R statistics software, and testing the solutions by the coefficient of determination R2 and the RMSE measure. Our results provided a good adaptation of the proposed model to the different datasets, satisfying the equality of variances, and also showing a robust fit when adding noise. Moreover, our model presented several advantages over the others, regarding the mentioned characteristics. This suggests that the power-law exponential model is a variant that adds new attributes to the set of existing variogram models. & COPY; 2023 Elsevier B.V. All rights reserved.